YES

weighted path orer with linear polynomial on natural numbers:

  isnoc_A(x1) = x1 + 1
  cons_A(x1,x2) = x1 + 4
  tp2_A(x1,x2) = 3
  nil_A = 1


precedence:

  tp2 > isnoc > nil > cons


status:
isnoc: [1]
cons: [1]
tp2: []
nil: []

the condition isnoc(nil()) ->> tp2(x3,x4) is unsatisfiable for all substitutions.